不定度规量子场论与算子代数
Indefinite-metric quantum field theory and operator algebra
摘要：
在量子场论中，常常不可避免地要引入不定度规空间.有一个问题，以确定度量结构的一个给定的表示空间的字段运营商。我们展示了系统的方法来确定这样的不定度量明确。首先，我们选择一个新的场算子对合$*$来代替原来的对合$\sdag$，使得存在一个Hilbert空间$({\cal H},<\cdot|\cdot>)$，它具有与$*$一致的正定度量$<\cdot|\cdot>$.其次，我们在${\cal H}$上找到另一个厄米形式$(\cdot|\cdot)$，使得$({\cal H},(\cdot|\cdot))$是Krein空间，并且$(\cdot|\cdot)$与$\sdag$相容.我们将这种方法应用到各种模型，并表明我们的结果与已知的结果一致。
英文摘要：
It is often inevitable to introduce an indefinite-metric space in quantum field theory. There is a problem to determine the metric structure of a given representation space of field operators. We show the systematic method to determine such indefinite-metric explicitly. At first, we choose a new involution $*$ of field operators instead of the original involution $\sdag$ such that there is a Hilbert space $({\cal H},<\cdot|\cdot>)$ with the positive-definite metric $<\cdot|\cdot>$ which is consistent with $*$. Next we find another hermitian form $(\cdot|\cdot)$ on ${\cal H}$ such that $({\cal H},(\cdot|\cdot))$ is a Krein space and $(\cdot|\cdot)$ is consistent with $\sdag$. We apply this method to various models and show that our results coincide with known results.
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